> What notation of the subspace of f (where f may be topological, uniform, > metric, etc. space) generated by a set X is better:> There's standard notation for a function f with it's domain restricted to a set A, namely f|A as rendered in ascii.

> 1. Subspace(f;X)> The choice of f for a space is extremely bad for f is usually used for functions. If S is a space and A subset S, then S|A is the subspace A,ie. S restricted to A.

> 2. SubSpace(f;X)> Ditto.

> 3. fill your own notation> > The notation f|_X is already taken for an other (however related) thing.>